Quantum Collision Theory of Nonrelativistic Particles: An Introduction

ISBN-13: 9783662655900 / Angielski / Miękka / 2023 / 224 str.

Reiner M. Dreizler; Tom Kirchner; Cora S. Lüdde

Opis

This book introduces the scattering theory of nonrelativistic systems, a standard tool for interpreting collision experiments with quantum particles at energies not too high. The goal is to explore the interaction between particles and their properties. The authors cover the basics of the theory through a detailed discussion of elastic scattering using the stationary Schrödinger equation and the Lippmann-Schwinger equation. These remarks are supplemented by a consideration of the time-dependent formulation of scattering theory. Selection rules for effective cross sections due to symmetries conditioned by the structure of the interparticle forces and the scattering of spin-polarized particles are discussed. The foundations for the treatment of inelastic processes are laid and explained by application to three-body and nucleotransfer processes.In all chapters, the more technical, mathematical aspect and the more physics-oriented explanations are separated as far as possible. The explanations are well comprehensible and suitable to introduce the reader to the physics of impact processes.

This book is a translation of the original German 1^st edition Streutheorie in der nichtrelativistischen Quantenmechanik by Reiner M. Dreizler, Tom Kirchner & Cora S. Lüdde, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). The present version has been revised extensively with respect to technical and linguistic aspects by the authors. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Spis treści

1 Elastic scattering: stationary formulation - differential equations.- 2 Elastic scattering: stationary formulation - integral equations.- 3 Elastic scattering: time-dependent formulation.- 4 Conservation laws in scattering theory.- 5 Elastic scattering: the analytical structure of the S-matrix.- 6 Elastic scattering with spin-polarized particles.- 7 Remarks on multichannel problems.- Bibliography.

O autorze

Reiner M. Dreizler

Studied physics in Freiburg/Breisgau (Diploma) and at the Australian National University, Canberra (Ph.D.). Research Associate and Assistant Professor at the University of Pennsylvania in Philadelphia. Professor of Theoretical Physics at the Goethe University, Frankfurt/Main. Holder of the S. Lyson Endowed Professorship until retirement. Member DPG, EPS, Fellow APS. Field of research: many-body systems of quantum mechanics.

Tom Kirchner

Studied physics at Goethe University, Frankfurt/M (diploma and doctorate). Postdoctoral researcher at York University, Toronto, Canada and at the Max Planck Institute for Nuclear Physics, Heidelberg. After a junior professorship in Theoretical Physics at TU Clausthal, return to York University, first as Assistant Professor, currently as Associate Professor. Member DPG, CAP, Fellow APS. Field of work: quantum dynamics of multi-particle coulomb systems, in particular atomic scattering processes.

Cora S. Lüdde

Studied physics at the Goethe University, Frankfurt/Main (diploma). After family break, re-entry into physics and computer science with focus on computer arithmetics. Experience and further education in didactics. Member of DPG. Field of work: application-oriented programming, creation of physics didactic software.

Blurb

This book introduces the collision theory of nonrelativistic quantum systems, a standard tool for the exploration of the interaction between quantum particles and their properties. The authors cover the basic elements of the theory by a detailed discussion of elastic scattering on the basis of a stationary formulation in terms of differential and integral equations as well as a time dependent formulation leading to S-matrix theory. An extension to the treatment of inelastic processes with a many channel situation is outlined and illustrated by an application to three-body and nuclear transfer processes. Special emphasis is laid on the discussion of selection rules due to different symmetries of the interaction between the particles and the scattering of spin-polarised particles in separate chapters.

Specific mathematical details are presented in separate sections at the end of each of the seven chapters in order to maintain the flow of argumentation concerning the actual aspects of the physics of collision processes.

This book is a translation of the original German 1st edition Streutheorie in der nichtrelativistischen Quantenmechanik by Reiner M. Dreizler, Tom Kirchner & Cora S. Lüdde, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). The present version has been revised extensively with respect to technical and linguistic aspects by the authors. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

The Authors

Reiner M. Dreizler, Professor emeritus of Theoretical Physics at Goethe University, Frankfurt/Main,works on many-body systems in quantum mechanics.

Tom Kirchner, Professor of Physics at York University, Toronto, Canada, works on quantum dynamics of multi-particle Coulomb systems, in particular atomic scattering processes.

Cora S. Lüdde, Diplom-physicist, research associate at Goethe University, Frankfurt/Main, Germany, working on application-oriented programming, researches computer arithmetic.